In our paper on exploring the universe, some of our probes required huge quantities of reaction mass in order to decelerate on arrival.

This is due to the tyranny of the rocket equation: to decelerate our final mass by , we need an initial mass so that:

  • , where is the exhaust velocity.

Given this equation, the initial mass needed grows as exponential in the required deceleration .

The relativistic rocket equation is similar but even worse, with an extra term in it.

So the most effective way of allowing high speed exploration of the universe is to somehow get around the rocket equation. I was vaguely thinking about ways of using the target galaxy or solar system to do that - maybe the probe could scoop up interstellar dust or use gravity slingshots. But I realised that we can get around the rocket equation more directly.

Decelerating with guns

Suppose you are shooting through space, and you want to decelerate by pointing a gun in the direction of travel. Because of relativity, we can consider that you are at rest, and that you are accelerating by shooting a gun in an opposite direction.

You have two bullets, and you can shoot the bullets sequentially or simultaneously; imagine that you had two guns strapped together. If you shoot the bullets one after another, the first will start moving at velocity of while you recoil at some . Then when you shoot the second bullet, it will start moving at (if we stay in the classical model for the moment). So the total backwards momentum is , where is the mass of a bullet.

If you fire the bullets simultaneously, the total backwards momentum is , however, and . By conservation of momentum, you will therefore be recoiling faster than if you shot the bullets sequentially.

What's happened? When you shot the bullets sequentially, part of recoil of the first bullet went into moving the second bullet at the same speed as you, which you actually didn't want. When you shot both bullets together, the recoil of both went purely to moving you. Therefore simultaneous fire is more effective at accelerating/decelerating. The real tyranny of the rocket equation comes from the fact that the early fuel needs to move the later fuel that needs to move the even later fuel. And most of that momentum gain is completely wasted: we don't actually care that exhaust fuel has gained momentum through the process. We'd like that extra momentum to be applied to the payload or probe, not to the fuel.

In practice: laser and solar sail

So there's a theoretical way around the rocket equation; can we do this in practice? Expending all fuel simultaneously would help (the equivalent of shooting all your bullets at once), but that extreme discharge might tear the probe and the rocket to pieces.

In space, there's no difference between the gun and the bullet - they're both just pieces of mass that fly off in opposite directions due to an explosion. So now imagine that there are ten thousand guns, floating independently in space, pointing at you. Everything is at rest with each other, and all the guns will fire in some sequence, and you will catch all the bullets (completely inelastic collision). Assume each gun, of mass , will recoil with velocity . Then the guns will have a total momentum of , and, by conservation of momentum, you and the bullets will have the same momentum in the opposite direction. If the mass of the bullets (and you) is small compared to , this will be an effective way of accelerating you. And note that your total final momentum depends on your mass, the mass of the bullets, the number of guns, , and . So it does not depend on the guns being fired at the same time, or any details of when they were fired. As long as you can catch every bullet, your final acceleration/deceleration will be the same. So you don't need to burn all your energy at once.

Catching bullets is hard, and we want to minimise their mass. So it's even better if we do this with lasers! Unfurl a solar sail around yourself, and have ten thousand free-floating lasers shoot at you in some sequence. This will gain you all the momentum of the lasers, independently of the sequence of firing.

The only real practical consideration is that you can cool down fast enough that each laser can fire before your sail moves out of their focus range; but a bigger sail can make both cooling and long distance firing easier.

Extra, theoretical, efficiency

What if your sail doesn't perfectly absorb all the laser light, but reflects some of it back? That's even better! In terms of bullets, that's the equivalent of elastic collisions, and you'll accelerate/decelerate even faster, losing less energy. Think in terms of conservation of momentum again: some light is now moving backwards, away from you. This can only happen if you've yourself gained some forward momentum.

In fact, the perfectly efficient way of decelerating would be for you to deploy a giant mirror, and for a single giant laser to do the same, then for the laser to blast you. The laser beam would bounce back between your mirror and the laser's mirror, gradually getting redshifted as you and the laser move faster and faster apart. This setup preserves both momentum and energy, and is the most perfectly efficient way of decelerating - and it doesn't depend on how fast the laser fires, a slow burn reaches the same conclusion as a swift burst. Why? Because conserving energy and momentum dictates the speeds at which you and the laser will end up.

Of course, in practice, the mirrors would not be perfectly reflective, the beam would lose focus, there would be some cosmic dust, and so on. Still, it's interesting to note that, in theory, we can completely do away with the rocket equation and accelerate/decelerate in the most efficient way possible, while using up energy arbitrarily slowly to do so. This hints that there may be practical methods that could get very efficient as well.

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16 comments, sorted by Click to highlight new comments since: Today at 12:22 PM

The qualitative explanation of the rocket equation here is very clear!

Avoiding carrying fuel with you is certainly tempting, solar sail and various beam-powered types of propulsion are some of the better known ones. Various types of the solar wind sail would give much more thrust if one could figure out how to efficiently stop or deflect the solar wind particles (mostly protons), and various versions of a ramjet when in interstellar space. is a decent summary. My bet is on that kind of technology, unless someone revolutionizes space travel by figuring out how to bend spacetime more efficiently than with sheer mass, and makes something like the Alcubierre drive feasible.

>unless someone revolutionizes space travel by figuring out how to bend spacetime more efficiently than with sheer mass, and makes something like the Alcubierre drive feasible.

The bigger problem here is just that genuine negative inertial mass (which you need for warp drives) is considered to be probably impossible for good reason, since it lets you both violate causality and create perpetual motion machines.

This is not directly related to the post, but while reading the paper a thought struck me and I wanted to get it down:

  • We apply the mediocrity assumption to the Earth among planets; we should also apply it to intelligence among processes.
  • The only intelligence we know of currently runs on chemical processes.
  • All chemical processes I know of naturally terminate.
  • The mediocrity assumption therefore says an intelligence process will also naturally terminate.
  • I therefore suspect a late filter.

Note: the Filter might not exist. In a nutshell, the Fermi paradox can be dissolved by realizing that "average number of civilizations per galaxy" is less important than "probability of galaxy containing single civilization". (Note: depending on your anthropics, this may or may not actually dissolve the paradox.)

Yes, I should amend that to "I suspect a late filter, if one exists."

Wait. You don't know enough chemical processes if you think they all (or even most) terminate naturally, except when their energy source runs out. I find it easy to believe that chemical processes much like the ones I comprise will be functioning many eons in the future. What part of "self-replicating DNA-like organization of chemical compounds" do you claim has a natural termination point?

except when their energy source runs out

There aren't any chemical processes for which this is not a problem. For complex ones like DNA, it is more of a problem rather than less because the absence of any one of the multiple required inputs will do it. A process needs a system, and all the systems with which we are experienced have limits. We also have several known candidates for catastrophic disruption to DNA-like processes, in the form of X-risk.

The problem boils down to whether we can keep jumping up to a larger system level before we deplete or disrupt the one we currently occupy; I see no reason to assume this will always succeed, even if the probability turns in our favor.

One way for the deceleration is a black hole close flyby where it's gravitation and powerful magnetic field could be used by the probe's magnetic sail. But from practical point of view, it unlikely to work, as the probe will be damaged by intense radiation.

However, my favorit method is to send multiple probes with slightly different speeds by a nanoprobe's accelerator. The first probe have v-nx speed, the next probe has v-(n-1)x speed and the last probe has the speed v. The difference x is so small that all the probes will reach each other near the target and clump in one large object. All this mass gain is used to built an accelerator-gun which send a nanoprobe with the speed -v, that is back, and this probe will have the near zero speed at the rest frame.

Hum, what does this gain over sending out all the probes in one clump from the start?

The size and price of the accelerator. For example, aliens have an accelerator which could send 1mg probe every second, and the accelerator's weight is 1000 tons. Thus, it will send its own mass in 20 000 years. All these probes clump (using some internal navigation and small difference in initial speed) with each other after a few million years, and using some nanotech, they build another accelerator, which send just one probe in the back direction, which is the deceleration, as its speed will be zero.

To send all the probes simultaneously, one need to build a trillion of such accelerators. However, this seems to be achievable even with one Dyson sphere. So clumping make sense only if there are some limits on the size of the accelerators.

Also, any intergalactic probe will experience "natural" deceleration because of expanding universe, similar to red shift, so the back-accelerator may be small than the sending accelerator.

What is a "magnetic sail"? That sounds interesting. Is it just a large electromagnet?

I don't understand your second method either. What is a nanoprobe? What is an accelerator? You're saying there's a small thing in space which can push things? Then you send many probes (which may or may not also be nanoprobes) to the same point. Then something happens involving an "accelerator gun", and now a (new?) nanoprobe is traveling backwards at the same speed at which the original probes were traveling forward? And it has "near zero speed at the rest frame" - the rest frame of what? Its own rest frame? But everything is at rest in its rest frame! And what's the motivation? If you can launch things forward at speed v, can't you just launch things backward at that same speed? How do we benefit from this setup?

Copied form the comment above: aliens have an accelerator which could send 1mg probe every second, and the accelerator's weight is 1000 tons. Thus, it will send its own mass in 20 000 years. All these probes clump (using some internal navigation and small difference in initial speed) with each other after a few million years, and using some nanotech, they build another accelerator, which send just one probe in the back direction, which is the deceleration, as its speed will be zero.

Nanoprobe is a small starship send by an accelerator, which is similar to electric railgun or hadron collider.

All nanoprobes are send in the same direction.

They are send with the different speeds, in such a way, that later nanoprobes are quicker and will catch up the first ones is some moment in time. They couple each over at that moment. This results in "clumping".

Resulting large clump of matter which itself is traveling with near с speed reorganise itself in a large starship using nanotech.

This starship builds another accelerator which sends one nanoprobe in the back direction with speed near c.

Rest frame is the frame of the first accelerator here, that is, of the alien civilisation.

The new nanoprobe has 0 speed relative to alien civilisation, but is now located millions light years from it, so the task of deceleration is solved.


Typical magnetic sail uses magnetiс field generated by the spacecraft to capture stellar wind.

This could be also used for deceleration by interaction with interstellar plasma.

But I thought about different thing: to use the magnetic field of the black hole for deceleration. In this case, the space craft generates its small magnetic field which interacts with giant magnetic field of the black hole.

Thanks for explaining. I see what you mean now. But I still don't get how this is useful. Why not simply send the larger ship in the first place, instead of sending the building materials?

Perhaps it's easier to accelerate smaller things? You can give the nanoprobe all the necessary momentum in the solar system - it doesn't have to carry any fuel - whereas you can't feasibly accelerate an entire ship to near-c within the solar system.

Yes, it is about price: this scheme will be a trillion times cheaper, as I discuss in a comment above. A super-intelligent alien AI may not worry about prices, but if it has some resource limitations, it would use more economical solutions.